Degrees of Crystallinity

In the previous sections we've worked with perfect "single" crystals - atoms are positioned in unit cells, and these unit cells are repeated in space to produce regular arrays of atoms at the macro scale. While this ideality is approximately true in some highly engineered materials (semiconductors) and some natural materials (gems, in particular) - this level of perfection is not true in general for materials. Feel free to read the text or watch the video supplement (Section 5.13.2).

We can generally classify a material's atomic arrangements via its degree of crystallinity in one of three ways:

• Single Crystal: This is a highly ordered structure in which atoms are located in predictable positions over their entire volume. These structures have both predictable short-range order (at the scale of the bond) and long-range order (at the scale of micrometers or more. In engineering applications, these are somewhat rare - but we do use single crystals in applications such as semiconductors, technical ceramics, superalloys, etc. Often the performance required by the application requires high degrees of predictability or perfection within the crystal. Figure 5.13.1(a.) shows a cartoon of atomic arrangement we'd see in single crystals.
  
  Single crystal materials possess properties that vary with direction because the anisotropy of the unit cell itself translates to macroscopic scales due to the long range order. These materials are often expensive to make and require complex processing.
• Polycrystalline Polycrystalline materials are those that have predictable short-range order (at the scale of the bond) and some degree of long-range order - but nothing that nears the degree of single crystalline materials (Figure 5.13.1(b)). The small crystallites that constitute polycrystalline materials will, at some point in the structure, become misaligned with neighboring crystallite. This leads to a defect in the crystal called a grain boundary. Most metals and conventional ceramics are polycrystalline, with some very specific expectations (alloys used in turbine blades).
  
  While polycrystalline material are made up of lots of small single crystal grains, all of these grains are randomly arranged through the materials volume, typically imbuing the material with isotropic properties. Compared to single crystals, polycrystalline materials or typically cheaper and require simpler processing.
• Amorphous materials are those that have essentially no predictable long-range order beyond the distance of a single bond (Figure 5.13.1(c.)). We call these materials amorphous because they are "without the form" that we observe in crystalline materials (a- means without and -morph means shape or form). They do not have any periodic long-range packing. Typical materials that are amorphous are glasses and many polymers.
  
  Because there is no crystal structure, amorphous materials possess isomorphous properties. They have broad applicability in engineering and commerce, and are relatively inexpensive to produce

One way to visual this structure is to present a so-called radial density map (Figure 5.13.2). In this map, we show the density of atoms ($g$) some distance $r$ away from a center atom. This communicates the difference in periodic regularity between (e.g.) and nanocrystalline material (Figure 5.13.2(a.)) in which there's clear, predictable, and regular order on the order of nanometers and an amorphous material Figure 5.13.2(b.), which only possess discernable order within its coordination shell and a bit beyond. Then, the disorder inherent to the structure essentially makes any regular pattern disappear.